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Proof step 50 from proof replayorphans-prepost (previous step)

ro1.inodes?, ks0.inodes?, inodekey(ino) ∈ ro1, inodekey(ino0) ∈ ro1, datakey(ino, n) ∈ ri0, inodekey(ino0) ∈ ks0, inodekey(ino) ∈ ks0, ks0 ⊆ ro1, ∀ key1. (key1 ∈ ri0 ∧ ¬ key1 ∈ ks0 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ks0) ↔ key1 ∈ ri1 ∧ ¬ key1 ∈ ro1 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ro1)) ∧ (key1 ∈ ri0 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ks0 ⊃ (∅)[key1];(key1 ∈ ks0 ⊃ (∅)[key1];ri0[key1])) = (key1 ∈ ri1 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ro1 ⊃ (∅)[key1];(key1 ∈ ro1 ⊃ (∅)[key1];ri1[key1])) ⊦ # ks0 = 0, # ro1 = 0, (ino ≠ ino0 ⊃ (∅)[datakey(ino, n)];(∅)[datakey(ino0, n)]) = (∅)[datakey(ino, n)], ks0 = ∅, ro1 = ∅

Proof step 50 from proof replayorphans-prepost (previous step)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

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